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为研究固体发动机药柱的损伤粘弹性行为,针对一种耦合损伤的三维非线性粘弹性本构模型,采用积分算法对其进行了数值离散,导出了本构方程的增量有限元形式。针对该增量型本构方程对应的非线性方程组,建立了采用Newton-Raphson迭代法求解的应力更新方法,并基于Abaqus软件和Fortran语言开发了相应材料本构子程序,最后应用算例对所设计数值方法及程序进行了验证与分析。结果表明,本文有限元解与对应解析解吻合良好,保持了很高的精度,所设计方法及程序有效,可应用于实际型号发动机药柱损伤结构分析。
In order to study the damage viscoelastic behavior of solid propellant grains, a three-dimensional nonlinear viscoelastic constitutive model of coupling damage is discretized using the integral algorithm. The incremental finite element form of the constitutive equation is derived. Aiming at the corresponding nonlinear equations of the incremental constitutive equation, a stress update method based on the Newton-Raphson iterative method is established. Based on Abaqus software and Fortran language, the corresponding material constitutive subroutine is developed. Finally, The numerical methods and procedures are verified and analyzed. The results show that the finite element solution in this paper is in good agreement with the corresponding analytical solution and maintains high precision. The designed method and procedure are effective and can be applied to the analysis of the actual structure of the damaged column.